Inference from sample statistics and margin of error

Surveying every single person in a population is usually impossible, so researchers measure a sample and use the result to estimate the population value. The sample mean estimates the population mean; the sample proportion estimates the population proportion.

Every estimate comes with uncertainty. The margin of error captures that uncertainty: it gives a range around the sample statistic where the true population value is likely to fall. If a poll finds 62% support with a margin of error of 4%, the true support plausibly lies between 58% and 66%.

Two factors drive the margin of error down: increasing the sample size and decreasing the variability in the data. On the SAT, the most common lever is sample size — larger samples produce smaller margins of error because each additional data point adds information.

SAT questions in this area typically hand you a sample statistic and a margin of error, then ask which population values are plausible. The core skill is forming the interval statistic ±margin of error and checking whether a given value falls inside it.